Holstein–Primakoff (H‐P) Approach to Determine the Optical Response of Hybrid Optomechanical System Containing Multiple Quantum Dots

Abstract

A theoretical model is presented to study the hybrid optomechanical system comprising an ensemble of N number of quantum dots (QDs). Utilizing the Holstein-Primakoff (H-P) transformation formalism, the calculations become easily scalable. The bistability in this hybrid optomechanical system is studied in the presence of third order nonlinear 𝝌 (3) medium using the H-P transformation method and to verify the results, numerical method has also been utilized. It is also demonstrated that the system's parameters may be tuned to alter the bistability phenomenon and absorption spectrum's response, which exhibits both positive and negative absorption (emission). This alternative approach (H-P transform) is demonstrated to solve analytically the system containing multiple QDs in an elegant manner.